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EffectofinterfacialsolutesegregationonductilefractureofAl–Cu–Scalloys

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Acta Materialia 61 (2013) 1676–1690

Effect of interfacial solute segregation on ductile fracture ofAl–Cu–Sc alloys

B.A. Chen a, G. Liu a,⇑, R.H. Wang b, J.Y. Zhang a, L. Jiang a, J.J. Song a, J. Sun a,⇑

a State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, Chinab School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, China

Received 26 September 2012; received in revised form 21 November 2012; accepted 24 November 2012Available online 12 December 2012

Abstract

Three-dimensional atom probe analysis is employed to characterize the Sc segregation at h0/a-Al interfaces in Al–2.5 wt.% Cu–0.3 wt.% Sc alloys aged at 473, 523 and 573 K, respectively. The interfacial Sc concentration is quantitatively evaluated and the changein interfacial energy caused by Sc segregation is assessed, which is in turn correlated to yield strength and ductility of the alloys. Thestrongest interfacial Sc segregation is generated in the 523 K-aged alloy, resulting in an interfacial Sc concentration about 10 timesgreater than that in the matrix and a reduction of �25% in interfacial energy. Experimental results show that the interfacial Sc segre-gation promotes h0 precipitation and enhances the strengthening response. A scaling relationship between the interfacial energy and pre-cipitation strengthening increment is proposed to account for the most notable strengthening effect observed in the 523 K-aged alloy,which is �2.5 times that in its Sc-free counterpart and �1.5 times that in the 473 and 573 K-aged Al–Cu–Sc alloys. The interfacialSc segregation, however, causes a sharp drop in the ductility when the precipitate radius is larger than �200 nm in the 523 K-aged alloy,indicative of a transition in fracture mechanisms. The underlying fracture mechanism for the low ductility regime, revealed by in situtransmission electron microscopy tensile testing, is that interfacial decohesion occurs at the h0 precipitates ahead of crack tip and favor-ably aids the crack propagation. A micromechanical model is developed to rationalize the precipitate size-dependent transition in frac-ture mechanisms by taking into account the competition between interfacial voiding and matrix Al rupture that is tailored by interfacialSc segregation.� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Aluminum alloys; Solute segregation; Fracture mechanism; Interfacial decohesion; Precipitate

1. Introduction

Aluminum alloys combine high strength and light weightand are thus of utmost importance as structural materials. Inparticular, heat-treatable Al alloys, which are strengthenedby the formation of precipitates, are used extensively in theautomotive and aviation industries [1]. The binary Al–Cusystem is a well-studied precipitation strengthening systembecause it forms the basis for a wide range of age-hardeningalloys. The precipitation sequence observed on aging these

1359-6454/$36.00 � 2012 Acta Materialia Inc. Published by Elsevier Ltd. All

http://dx.doi.org/10.1016/j.actamat.2012.11.043

⇑ Corresponding authors.E-mail addresses: lgsammer@mail.xjtu.edu.cn (G. Liu), junsun@

mail.xjtu.edu.cn (J. Sun).

alloys, supersaturated solid solution (SSSS)! Guinier–Preston (GP) zones! h00 ! h0 ! h, is often used as a modelsystem for describing the fundamentals of precipitationhardening [2].

Small additions of various alloying elements are ofprime importance in modifying the precipitation/micro-structure and improving the mechanical properties of Alalloys [3]. Such microalloying effects have also been appliedto the Al–Cu alloys [3–11]. Trace element or microalloyingadditions of Sn, Cd or In are well known to suppress low-temperature aging and enhance both the rate and extent ofage hardening at elevated temperature, by promoting theformation of h0 at the expense of GP zones and h00 [4,5].Two types of proposal have been offered to describe the

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B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1677

mechanisms for this microalloying effect. One is that the Sn(Cd or In) atoms segregate to the precipitate/matrix inter-face and lower the interfacial energy somewhat [5–7]. Thismechanism was first suggested [5] to account for the weakX-ray reflection observed during the early stages of aging,and subsequently received indirect experimental supportseparately from calorimetric measurements [6] and trans-mission electron microscopy (TEM) observations [7]. Theother proposal is that the trace elements facilitate heteroge-neous nucleation of h0, either directly at Sn (Cd or In)-richparticles [8] or indirectly at the dislocation loops present inthe as-quenched microstructure [9]. In a later study usingatom probe field ion microscopy [10], it was directlyrevealed that no Sn was segregated at the h0/a-matrix inter-face in the Al–Cu alloys with trace Sn addition. Clusters ofSn atoms were detected in as-quenched samples, and theformation of Sn clusters was clearly found to precede theformation of h0. These atom probe analyses indicated thatheterogeneous nucleation of h0; is the predominant microal-loying mechanism in the Sn (Cd or In)-modified Al–Cualloys. Similarly, the heterogeneous nucleation mechanismis also responsible for the recent findings [11,12] that minoradditions of Si and Ge in Al–Cu increases hardness andproduces a fast hardening rate when aged at elevated tem-perature, where the first formed Si–Ge precipitates providepreferential nucleation sites for metastable h00 and then forh0 phases.

The addition of a minor amount of Mg in Al–Cu alloys,however, was found [13] to promote low-temperature aging,i.e. increasing the response on natural aging. The mecha-nism was suggested [13] to be that Mg atoms preferentiallytrap quench-in excess vacancies to retard Cu cluster forma-tion in the initial aging stage. In the following aging stage,complex Cu/Mg/vacancy clusters are formed and act aseffective nucleation sites for GP zones. The formation ofCu/Mg/vacancy complex clusters greatly retards the clustergrowth and increases the cluster number density, accountingfor the enhancement in the natural aging response.

Most recently, segregations of Si and Mg atoms at h0/matrix interfaces have been visibly revealed in Al–Cu alloyswith minor Si and Mg additions [14,15], by using theadvanced three-dimensional atom probe tomography(3DAP). The solute atom segregation will change the inter-facial conditions (e.g. interface structure, chemistry compo-sition and energies) and cause a series of evolutions in bothprecipitation behaviors and strengthening responses,including precipitate nucleation and concomitantly numberdensity and driving force for precipitate coarsening [16].Solute segregation at precipitate/matrix interfaces is animportant microalloying method to tailor the precipitationand improve the hardening response.

Previous investigations of the microalloying effect aremainly focused on the underlying mechanisms and harden-ing response. Little attention has been paid to the influenceof minor microalloying elements on ductile fracture of Alalloys. As a type of structural material for technological

applications, the Al alloys should have not only highstrength but also excellent ductility. The addition of micro-alloying elements will inevitably affect the deformationcapability and ductility of the Al alloys through changingthe size, number density, distribution and even interfacialconditions of precipitates. On the one hand, the morehomogeneous distribution of finer precipitates caused bythe microalloying effect can relieve local stress/strain con-centration during deformation and therefore increase theductility. On the other hand, the presence of microalloyingelements may lead to the deterioration in the ductility of Alalloys, such as by forming coarse constituent and addi-tional other second phase particles [17,18], and/or bychanging the precipitate/matrix interfacial conditions whensegregating at the interfaces. Competition between theseopposite effects will determine the deformation behaviorsof the microalloyed Al alloys, which needs to be under-stood in order to aid the further design of advanced Alalloy.

In this paper, systematical studies were performed toinvestigate the effect of minor Sc addition on microstruc-tural evolution, hardening response and especially ductilefracture of Al–Cu mode alloys. Al–Cu–Sc was chosen forthe study because (i) our primary experimental results haveshown [19] that the addition of trace amounts of Sc inAl–Cu alloys remarkably promotes the homogeneous pre-cipitation of h0 and greatly reduces the precipitate size, dis-playing a significant microalloying effect; (ii) highlycoarsening-resistant Al3Sc particles (e.g. coarse primaryAl3Sc, intermediate Al3Sc dispersoids and fine Al3Sc precip-itates; see Fig. 1) will be formed additionally [20], which canimprove the high temperature performance of Al–Cu-basedalloys and extend their applications; (iii) the binary Al–Cualloys are a typical type of plate-like precipitate-containingaluminum alloys, which have attracted extensive theoreticalstudies on precipitation thermodynamics, kinetics andstrengthening. They are also ideal mode materials for inves-tigating the microalloying effect on ductile fracture.

2. Experimental procedures

2.1. Material preparation and heat treatments

Alloys with a composition of Al–2.5 wt.% Cu alloys(abbreviated Al–Cu alloys), Al–2.5 wt.% Cu–0.3 wt.% Sc(Al–Cu–Sc) and Al–0.3 wt.% Sc (Al–Sc) were respectivelymelted and cast in a stream argon, by using 99.99 wt.%pure Al, 99.99 wt.% pure Cu and mast Al–2.0 wt.% Scalloy. The cast ingots were homogenized at 793 K for24 h and hot extruded at 723 K into plates 14 mm in thick-ness and 60 mm in width. All the plates were subjected tothe same heat treatments, i.e. solutionized at 863 K for3 h, followed by a cold water quench and subsequentlyaged at 473 K, 523 K and 573 K, for a series of times.The maximum error of all the temperature measurementsin the present experiments was ±1 K.

Fig. 1. Representative TEM images and 3DAP map showing multiscaled Sc-based particles and clusters (pointed by arrows) in present Al–Cu–Sc alloys,i.e. primary Al3Sc particles in micrometer size (a), Al3Sc dispersoids in sub-micro size (b), Al3Sc precipitates in nanometer size (c) and Sc cluster in atomiclevel (d) (green = Al atoms, orange = Cu atoms, blue = Sc atoms, dimensions: 20 � 20 � 30 nm). (For interpretation of the references to color in thisfigure legend, the reader is referred to the web version of this article.)

1678 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

2.2. Microstructural characterizations

Microstructures of the alloys were characterized by usingtransmission electron microscopy (TEM) and high-resolu-tion TEM. TEM foils were prepared following standardelectro-polishing techniques for Al alloys. Quantitative mea-sures of the number density and size of the precipitates werereported as average values of more than 200 measurements.Volume fraction of the second phase particles was deter-mined by employing the corrected projection method[21,22], where the foil thickness of each captured regionwas obtained through convergent beam electron diffractionpatterns [23]. Using the raw radius data of precipitates andthe foil thickness in each area, the radius distributions werecalculated after correction for the truncation effects based ona method by Crompton et al. [24]. Details about the mea-surements on precipitates, dispersoids and constituents aregiven in our previous publications [17,18,21,25].

In order to visibly reveal the microalloying mechanismat atomic level, 3DAP experiments were performed usingan Imago Scientific Instruments 3000HR local electrodeatom probe (LEAP). APT sample blanks with a squarecross-sectional area of �300 � 300 lm2 and a 1 cm lengthwere prepared by a combination of slicing and mechanical

grinding. A two-step electropolishing procedure was usedfor making tips from these blanks [26,27]. A 10 vol.% per-chloric acid in methanol solution was used for coarse pol-ishing, and the final polishing was performed using asolution of 2 vol.% perchloric acid in butoxyethanol.APT data collection using the electrical pulsing mode wasperformed at a specimen temperature of 30 ± 0.3 K, witha voltage pulse fraction (pulse voltage/steady-state DCvoltage) of 20%, a pulse repetition rate of 200 kHz and abackground gauge pressure of <6.7 � 10�8 Pa (5 �10�10 torr).

2.3. Measurements of mechanical properties

Tensile testing was used to measure yield strength (r0)and strain to fracture (ef) of the alloys. Smooth dog-bone-shaped tensile specimens have a gauge size of 6 mmin diameter and 30 mm in length, with their axis alongthe extrusion direction. The testing was performed at aconstant strain rate of 5 � 10�4 s�1 with the load directionparallel to the specimen axis. The yield strength was deter-mined as the 0.2% offset and the strain to fracture wasdetermined as ef = ln (Ao/Af), where Ao is the initial areaand Af is the area at fracture of the specimens.

B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1679

3. Results

3.1. Microstructures of Al–Cu and Al–Cu–Sc alloys

Previous publications have reported that the addition ofSc in Al alloys may lead to the formation of primary Al3Scintermetallic phase [28,29] and Al3Sc dispersoids [30,31],besides the Al3Sc precipitates. In present work, both primaryAl3Sc (Fig. 1a) and Al3Sc dispersoids (Fig. 1b) have beenobserved in the Al–Cu–Sc alloys. Quantitative measure-ments show that the primary Al3Sc particles and Al3Sc dis-persoids have an average size of 0.6 lm and 50 nm, and avolume fraction of �0.51% and 0.12%, respectively. TheAl3Sc dispersoids are especially effective in hindering thegrain growth through Zener-drag action [30]. Besides, thepresence of primary Al3Sc can also refine the grains by pro-moting the heterogeneous grain nucleation [29]. These canwell explain the present results that the as-quenched Al–Cu–Sc alloys have grains (in pancake shape with width of�110 lm and length of �800 lm) smaller than their Sc-freeAl–Cu counterparts (width�180 lm and length�1300 lm).During the aging treatment, there is negligible change in thepre-existing microstructural characteristics of grains, pri-mary Al3Sc and Al3Sc dispersoids, due to the relative lowaging temperature. The apparent microstructural evolutionis only the nucleation and growth of precipitates. Therefore,the aging-dependent strength and ductility are merelyrelated to the precipitation, and the effect of grain size, pri-mary Al3Sc particles and Al3Sc dispersoids, can be ignored.

Fig. 2 shows representative TEM images to demonstratethe size and distribution of h0 precipitates before and afterSc addition in the Al–Cu alloys, aged at three different tem-

Fig. 2. Representative TEM images showing the size and distribution of h0 precd), 523 K (b and e), and 573 K (c and f), respectively.

peratures for the same duration of 3 h, respectively. It canbe visibly found that, at any aging temperature, the h0 pre-cipitates in Al–Cu–Sc alloys always have a reduced size andincreased number density compared with those in the Al–Cu alloys. This indicates that the Sc addition promotesthe homogeneous precipitation of finer h0 in Al–Cu alloys,displaying a typical microalloying effect.

Statistical measurements on the radius (rp) and thickness(hp) of the plate-shaped h0 before and after Sc addition havebeen carefully conducted and the results are plotted inFig. 3a–d as a function of aging time (t in s), respectively.It is quantitatively shown that (i) the Sc addition causes an�20% decrease in both rp and hp when the aging tempera-ture (T) is 473 and 573 K; (ii) the decrease can reach �40–50% when T is 523 K; (iii) rp and hp in the T = 523 KAl–Cu–Sc alloys are close or even lower than those in theT = 473 K Al–Cu–Sc alloys. These hint that the microal-loying effect of Sc addition is closely dependent on agingtemperature and, among the three aging temperatures stud-ied here, the most pronounced effect is reached at the inter-mediate temperature of T = 523 K. The reason for thisextraordinary phenomenon will be proposed later whendiscussing the microalloying mechanisms.

The minor Sc addition in Al–Cu alloys can not only refinethe h0 precipitates but also narrow the h0 size distribution to alarge extent. This can be well illustrated by comparing theh0-size distribution between the Sc-free and Sc-added Al–Cu alloys, as representatively shown in Fig. 3e vs. Fig. 3fat T = 523 K and t = 3 h. The h0-size distribution is moreconcentrated in the Al–Cu–Sc alloys (Fig. 3f), indicative ofmore synchronous nucleation and growth of the h0 precipi-tates aided by the Sc atoms. However, the maximum volume

ipitates in the Al–Cu (a–c) and Al–Cu–Sc (d–f) alloys aged at 473 K (a and

102 103 104 105

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Al-Cu @ 523 K Al-Cu-Sc @ 523 K

0 200 400 600 800 1000Precipitate radius (nm)

102 103 104 105

102 103 104 105 102 103 104 105

102 103 104 105102 103 104 105

Fig. 3. Statistical results on the evolution of h0 precipitate radius (rp) and thickness (hp) with aging time (t) in Al–Cu (a and c) and Al–Cu–Sc (b and d)alloys aged at 473, 523 and 573 K, respectively. (e and f) are precipitate size distribution of Al–Cu and Al–Cu–Sc alloys aged at 523 K, respectively, forcomparison. (g and h) are t-dependent precipitate volume fraction and number density of Al–Cu and Al–Cu–Sc alloys aged at 523 K, respectively.

1680 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

fraction of h0 precipitates after peak aging is almostunchanged (Fig. 3g), which implies that the Sc additionhas negligible influence on the saturated solution of Cu inAl matrix or on the excess Cu atoms available for h0 precip-itation. The precipitation features characteristic of the Scmicroalloying effect in the present alloys mainly includerefined size (Fig. 3b and d), increased number density(Fig. 3h) and more uniform distribution (Fig. 3f).

Another issue of interest to note is that the thickness ofh0 precipitates is retained to below 8 nm even when exposedto 523 K for 12 h. The high coarsening resistance of h0 pre-cipitates was analyzed by using 3DAP examinations. Fig. 4shows 3DAP element maps of the Al–Cu–Sc alloys aged at

523 K for 3 h. A h0 precipitate is just oblique cross theexamined region, see the part assembled by Cu atoms(Fig. 4a–c). It seems that the Sc atoms roughly segregateat the h0/matrix interfaces. To obtain 3DAP maps withhigher spatial resolution and therefore to obtain moreaccurate data, local analyses were probed along the[00 1]a direction, i.e. in the direction normal to the broadsurface of the h0 plate. The cross-sectional element mapsare shown in Fig. 5a–d. The corresponding compositionprofile is displayed in Fig. 5e. The solid vertical line inFig. 5e indicates the location of the heterophase interfacebetween the a-Al matrix and the h0 platelet, which is atthe inflection point of the Al concentration profile. The

Fig. 4. 3DAP maps showing an oblique h0 precipitate and distribution of Al, Cu and Sc atoms in the Al–Cu–Sc sample aged at 523 K for 3 h (green = Alatoms, orange = Cu atoms, blue = Sc atoms, dimensions: 80 � 80 � 180 nm). Cu and Sc atoms are co-presented in (b), while only Cu atoms are presentedin (c) and only Sc atoms in (d). Sc segregation at the h0/matrix interfaces is visibly revealed. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

-12 -10 -8 -6 -4 -2 0 2 4-80

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573 K

(f) (e)

(a) (b)

(c) (d)

Fig. 5. 3DAP maps (a–d) typically showing distribution of Al, Cu, and Sc atoms across the h0/matrix interface in the Al–Cu–Sc sample aged at 523 K for3 h (green = Al atoms, orange = Cu atoms, blue = Sc atoms, dimensions: 20 � 20 � 40 nm). Cu and Sc atoms are co-presented in (b), while only Cu atomsare presented in (c) and only Sc atoms in (d). Sc segregation at the h0/matrix interfaces is definitely verified. Corresponding proxigram is shown in (e),where the solid vertical line indicates the location of the heterophase interface between the h0 precipitate and matrix. (f) shows the proxigram of Sc cross theh0/matrix interface in the Al–Cu–Sc sample aged at 473 and 573 K for 3 h, respectively. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1681

spatial concentration profiles of the h0 platelet and a-Almatrix are displayed on the right- and left-hand sides ofthis line, respectively. A high Sc concentration up to

0.8 at.% is shown at the interface, which is �10 timesgreater than the Sc concentration within Al matrix (esti-mated to be �0.08 at.% by subtracting the Sc atoms

1682 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

consumed for forming primary Al3Sc and Al3Sc disper-soids). This provides evidence to verify the noticeable Scaggregation at the broad face of the h0 precipitate. The h0

precipitates are well known [32] to possess a plate morphol-ogy with coherent interfaces to the a-Al matrix along itsbroad flat faces and semi-coherent interface at its periph-ery. Biswas et al. [15] have experimentally found that theMg and Si segregation at the semi-coherent interface ofh0 precipitate is a factor of two greater than at the coherentinterface, showing a stronger segregation potential at thesemi-coherent interface. Unfortunately in the present inves-tigations, no 3DAP detections have been encountered atthe semi-coherent interface, mainly due to the large sizeof h0 precipitates and hence the low probability of meetingthe semi-coherent interface.

Orientated plate-like precipitates, such as h0 in Al–Cu-based alloys, have been generally believed to thicken by aledge mechanism [33–35]. The overall thickening kineticswas commonly found to be somewhat slower than allowedby volume diffusion of the solute, which indicates an inter-face controlled mechanism. Since Sc atoms are segregatedat the h0/matrix interfaces, the motion of thickening ledgeduring the course of h0 growth must involve the simulta-neous flux of Cu from the matrix to the riser of the ledgeand the redistribution of Sc from the original broad faceof the h0 plate to the terrace of the migrating thickeningledge. This is similar to the growing process of X phasein Al–Cu–Mg–Ag alloys [35,36]. The diffusion coefficientof Sc in Al matrix is DSc = 1.9 � 10�4exp (� 164 kJ mol�1/RT) m2 s�1 [20], which is several orders less than thatof Cu (DCu = 4.4 � 10�5exp (�134 kJ mol�1/RT) m2 s�1)within the studied temperature range. So the Sc aggrega-tion at the h0/matrix interfaces may limit the Cu atom dif-fusion and thus restrict the precipitate growth.

Similarly, the cross-sectional composition profile of h0

precipitate in the Al–Cu–Sc alloys aged at 473 and 573 Kfor 3 h has been respectively examined. Fig. 5f presentsonly the Sc concentration across the h0/matrix interface.Sc aggregation at the interface is also clear in both thetwo samples. But the Sc concentration at interface is only�0.28 at.% (573 K) and �0.22 at.% (473 K), respectively,much less than that (�0.80 at.%) in the 523 K-aged alloys.These atom-level findings seem to agree with the experi-mental measurements on precipitate sizes, considering Sceffect on inhibiting precipitate growth as mentioned above.The most Sc aggregation causes the most reduction in pre-cipitate sizes in the 523 K-aged Al–Cu–Sc alloys, whilereduction in both the 473 and 574 K-aged alloys is rela-tively less because the interfacial Sc aggregation and con-comitant Sc inhibiting effect are weakened.

The most pronounced interfacial Sc segregationobserved in the 523 K-aged Al–Cu–Sc alloys is possiblyrelated to two requirements. One is that the Sc atomsshould have enough diffusion capability to migrate towardsthe h0/matrix interfaces. The other is that no Sc-based pre-cipitates will be formed in order to ensure enough free Scatoms available for interfacial segregation. The first

requirement can be achieved at relatively high aging tem-perature, while the second requirement needs a relativelylow aging temperature because the Al3Sc precipitates areready to nucleate when the aging temperature is above�573 K [28]. Simultaneous meeting of the two oppositerequirements results in an intermediate aging temperaturewhere it becomes the most significant Sc segregation ath0/matrix interfaces. This hypothesis can interpret thestrongest interfacial Sc concentration in the 523 K-agedAl–Cu–Sc alloys rather than in the 473 and 573 K-agedalloys. In the next section, this hypothesis will be partiallyverified by the microstructural observations in Al–Sc alloysaged at the corresponding temperatures.

3.2. Microstructures of Al–Sc alloys

TEM and 3DAP examinations have been performed inthe Al–Sc alloys aged at 473, 523, 573 and 673 K for 3 h.No precipitates have been found at T = 473 and 523 K.Fig. 6a and b shows representative 3DAP images of the473 and 523 K-aged Al–Sc alloys, respectively. A largenumber of Sc clusters are clearly observed in the 523 K-aged alloy while only a small quantity of Sc clusters inthe 473 K-aged alloy are observed. Since the cluster forma-tion is controlled by the atom diffusion, it can be concludedthat the diffusion of Sc atoms is considerably limited at theaging temperature of 473 K, consistent with above hypoth-esis. When T is raised to 573 K, Al3Sc particles are precip-itated (see Fig. 6c). These particles have a diameter rangingfrom 1.5 nm to 7 nm, with an average diameter of �3 nm.The average diameter of the Al3Sc precipitates will increaseto �7–8 nm at T = 673 K (Fig. 6d). Due to the abundantformation of Al3Sc precipitates (e.g. number density of�2 � 1021 m�3 in the 573 K-aged alloy), Sc atoms remain-ing in the matrix are greatly reduced. This agrees withabove hypothesis that Sc atoms available for interfacialsegregation are limited once Sc-based precipitates formed.

3.3. Mechanical properties

Dependences of yield strength (r0) and fracture strain(ef) of Al–Cu and Al–Cu–Sc alloys on aging temperatureT are shown in Fig. 7a–d, respectively, as a function ofaging time t. Strength evolutions displayed in the presentAl–Cu alloys are similar to previous reports [21,37] thatthe peak strength is slightly reduced while the time topeak-aging point is shortened with increasing T (Fig. 7a).The ductility is generally lowered at higher T (Fig. 7c)because larger precipitates formed at higher T are apt toinduce local stress/strain concentration and hence causeearly rupture [38].

In contrast, the evolutions in both strength and ductilitybecome abnormal in the Sc-added Al–Cu alloys. The high-est peak strength is found in the 523 K-aged Al–Cu–Scalloy (Fig. 7b), which is increased by �30% and 50% incomparison with that of the 573 and 473 K-aged counter-parts, respectively. Besides, the 523 K-aged Al–Cu–Sc alloy

Fig. 6. 3DAP maps showing distribution of Al and Sc atoms in the Al–Sc alloys aged at 473 K (a) and 523 K (b) for 3 h (green = Al atoms, blue = Scatoms, dimensions: 20 � 20 � 30 nm). (c and d) are typically TEM images showing the Al3Sc precipitates in the Al–Sc alloys aged at 573 and 623 K for 3 h,as indicated by arrows. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1683

exhibits two extreme regions in the t vs. ef curve, i.e. thegreatest ef when t is less than a critical point of tcri � 1.5 h(or a critical precipitate radius of rcri

p � 200 nm), with thelowest ef thereafter (Fig. 7d). There exists a sharp drop inductility at the critical point, as marked in Fig. 7d. The473 and 573 K-aged alloys, however, show a gradualdecrease in ductility, radically different from what wasobserved in the 523 K-aged alloys.

It is easy to explain why the highest peak-aging strengthis observed in the 523 K-aged Al–Cu–Sc alloy, becausemicrostructural examinations have disclosed the mostreduction in precipitate sizes and simultaneously the mostpromotion in precipitate density in this alloy caused bythe most pronounced Sc effect. The refined precipitatesare generally believed [17,18,39,40] to reduce the deforma-tion discrepancy between the matrix and the precipitates,which will alleviate the local stress/strain concentrationand hence enhance the ductility. This can interpret thegreatest ductility in the first regime of rp < rcri

p , but cannotexplain the lowest ductility in the second regime of rp > rcri

p .The sharp decrease in ductility observed at rcri

p indicates asize-dependent transition in fracture mechanisms.

In situ TEM tensile testing was further performed on theT = 523 K and t = 3 h Al–Cu–Sc alloy in order to revealthe fracture mechanism in the rp > rcri

p regime. Fig. 8a cap-tures a crack at the rim of the TEM sample that is verticalto the direction of applied tensile stress. Two orthogonalvariants of h0 precipitates are dispersed ahead of the crack

tip. One variant of the precipitates is approximately paral-lel with the crack (defined P-type precipitates), while theother is almost vertical to the crack. Applying tensile stressprogressively, interfacial decohesion was observed at the P-type precipitates ahead of the crack tip, as typically shownin a magnified TEM image in Fig. 8b. Interfacial decohe-sion triggers interfacial microcracks, which will truncateprimary crack growth, preclude large accumulations ofstrain and result in low ductility. Fig. 8c and d shows rep-resentative TEM images indicating how the crack propa-gates along some matrix/precipitate interfaces, creatingorthogonal growth segments coincident well with the pre-cipitate orientations. In contrast, no interfacial decohesionand resultant crack propagation along the matrix/precipi-tate interfaces have been observed in the T = 523 K andt = 1 h Al–Cu–Sc alloy (within the rp < rcri

p regime) whensubjected to the same in situ TEM tensile testing. This hintsthat interfacial decohesion at the matrix/precipitate inter-face is responsible for the low ductility at the regime ofrp > rcri

p or t > tcri. A micromechanical model will be devel-oped in Section 4 to address the fracture behavior causedby the interfacial decohesion and analyze the critical condi-tion for interfacial decohesion.

One may wonder whether the Sc clusters or Al3Sc pre-cipitates should have predominant effect on the ductilefracture of the Al–Cu–Sc alloys, since the solute clusters[41–43] and Al3Sc particles [44–46] have been revealed tointeract with dislocations substantially and therefore affect

102 103 104 10550

100

150

200

250

300

t (s)

(a)Al-Cu 473 K 523 K 573 K

50

100

150

200

250

300 (b)Al-Cu-Sc

σ 0 (MPa

)

473 K 523 K 573 K

0.0

0.2

0.4

0.6

0.8

1.0(c)

Al-Cu

ε f

473 K 523 K 573 K

0.0

0.2

0.4

0.6

0.8

1.0

Sharp decrease(d)

Al-Cu-Sc 473 K 523 K 573 K

tcri

0.0

0.2

0.4

0.6

0.8

1.0(e)

673573523473

ε f

Aging temperature (K)

Al-Sc Al-Cu Al-Cu-Sc

0

50

100

150

200(f)

673573523473

Δ σ 0 (M

Pa)

Aging temperature (K)

Al-Sc Al-Cu Al-Cu-Sc

σ 0 (MPa

)

ε f

102 103 104 105

t (s)

102 103 104 105

t (s)102 103 104 105

t (s)

Fig. 7. Dependence of yield strength (r0) (a and b) and the strain to fracture (ef) (c and d) of Al–Cu (a and c) and Al–Cu–Sc alloys on aging temperature(T) as a function of aging time (t). T-dependent ef (e) and precipitation strength increment (Dr0 ¼ r0 � ri

0; where ri0 is the initial yield strength before aging

treatment) (f) of the Al–Cu, Al–Cu–Sc and Al–Sc alloys for comparison (t = 3 h).

1684 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

the strengthening response as well as deformation behav-iors. However, our experimental measurements on pureAl–Sc alloys show that there is no apparent change in theductility among the Al–Sc alloys peak-aged at 473, 523and 573 K, respectively (see Fig. 7e). A perceptible decreasein the ductility can be only detected at T = 673 K. Thisclearly indicates that neither the Sc clusters nor the fine Al3-

Sc precipitates predominantly affect the ductile fracture ofthe present Al–Cu–Sc alloys. It is the h0-related local defor-mation behaviors, including deformation incompatibilityand interfacial decohesion, that play a key role in the duc-tile fracture process and be responsible for the abnormalsharp decrease in ductility in the 523 K-aged Al–Cu–Scalloy.

Fig. 7f displays the yield strength increment (Dr0 ¼ r0

�ri0; where ri

0 is the initial yield strength before aging treat-ment) induced by age-hardening in Al–Cu, Al–Sc, and Al–Cu–Sc alloys aged at different T for 3 h, respectively. Themaximum Dr0|Al–Cu–Sc in the Al–Cu–Sc alloys occurs at523 K, while the maximum Dr0|Al–Sc in the pure Al–Sc alloyscomes at T = 573 K. This discrepancy hints that thestrengthening effect in the present Al–Cu–Sc alloys is not

predominantly contributed by Sc clusters or Al3Sc precipi-tates. It is because a large number of Sc atoms have been seg-regated at the h0/matrix interfaces in the Al–Cu–Sc alloys,and Sc clusters or Al3Sc precipitates therein are remarkablyreduced by compared with their Al–Sc counterparts (see thestatistical results in Table 1). The high Dr0|Al–Cu–Sc in the Al–Cu–Sc alloys is then believed to be mainly related to the h0-strengthening effect, given the significant reduction in h0 sizeand promotion in h0 density especially at T = 523 K.

4. Discussion

In the above section, we have presented experimentalresults that Sc atoms are prone to segregate at the h0/matrixinterfaces, which modifies the h0 nucleation/growth andimpacts on the strengthening response and fracture behav-iors. The Sc segregation effect exhibits a nonmonotonicaging temperature-dependence, resulting in the maximumstrengthening effect at T = 523 K while an unexpected lowductility is due to interfacial decohesion. In this section,reduction in h0/matrix interfacial free energy will be quanti-tatively evaluated by taking into account the interfacial Sc

Fig. 8. Representative images captured during in-site TEM tensile testing to show crack propagation aided by interfacial decohesion at h0/matrixinterfaces in the Al–Cu–Sc alloy aged at 523 K for 3 h. (a) shows a crack and the h0 precipitate distribution ahead of the crack tip before testing. Afterapplying external stress to some extent, some h0 precipitates ahead of the crack tip will suffer from interfacial decohesion. A magnified TEM image on theregion corresponding to the boxed part in (a) is displayed in (b) to visibly demonstrate the interfacial decohesion (indicated by closed arrows) andconcomitantly the formation of interfacial voids. Further increasing the applied stress, the main crack will propagate along the interfacial voids. (c and d)are representative images displaying the crack propagation along the matrix/precipitate interfaces and the creation of some orthogonal growth segments(indicated by open arrows) that are coincident well with the precipitate distribution. (d) is a magnified image of the region boxed in (c). Compared with (c),contrast is re-adjusted in (d) to show the h0 plates and their distribution more clearly.

Table 1Statistical results on the parameters of Sc clusters and Al3Sc precipitates in Al–Cu–Sc and Al–Sc alloys.

Alloys T (K) (t = 3 h) Sc clusters+ Al3Sc precipitate

Number density (1022 m�3) Size (nm) Number density (1021 m�3)

Al–Cu–Sc 473 0.35 ± 0.13 – –523 1.22 ± 0.45 – –573 – 4.1 ± 1.5 0.82 ± 0.31

Al–Sc 473 0.74 ± 0.23 – –523 4.16 ± 0.51 – –573 – 3.5 ± 2.2 2.04 ± 0.22

+ The minimum cluster size is Nmin = 10, the maximum separation distance dmax = 0.5 nm.

B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1685

segregation, which will be used to interpret the observedstrengthening effect on the basis of the maximum precipitategrowth rate hypothesis [47,48]. In addition, a micromechan-ical model will be developed to rationalize the abnormal duc-tile fracture caused by the size-dependent interfacialdecohesion in the 523 K-aged Al–Cu–Sc alloys.

4.1. Reduction in interfacial free energy caused by interfacial

Sc segregation

Si segregation at h0/a-Al matrix interfaces and Mg segre-gation at Al3Sc/a-Al matrix interfaces have been demon-strated by Seidman’s group [14,15,49,50] using atomprobe tomography. They also proposed a thermodynamicmethod for quantitative analyses of interfacial segregationof solute atoms across heterophase interfaces. Here, weadopt their analytical method to quantitatively assess the

reduction in interfacial free energy caused by the Sc segre-gation at the h0/a-Al matrix interfaces.

Following their treatments, the relative Gibbsian inter-facial excess is firstly determined to provide a quantitativethermodynamic evaluation for Sc segregation in the ter-nary Al–Cu–Sc alloys [51]:

CrelSc ¼ CSc � CCu

caAlc

h0

Sc � ch0

AlcaSc

caAlc

h0Cu � ch0

AlcaCu

� CAlca

Scch0

Cu � ch0

SccaCu

caAlc

h0Cu � ch0

AlcaCu

ð1Þ

where CrelSc is the Gibbsian interfacial excess of Sc relative to

Cu and Al; CSc, CAl and CCu are the Gibbsian interfacialexcess of Sc, Al and Cu, respectively; and ca

i and ch0

i arethe concentrations of an element (i = Al, Cu or Sc) in thea-Al matrix and h0 precipitates. Referring to a representa-tive proxigram as shown in Fig. 5e, the shaded areas inthe proxigram represent the individual Ci [14] and the

1686 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

values of Ci are determined using proxigram concentrationprofiles from

Ci ¼ qDxXq

m¼1

cmi � ck

i

� �ð2Þ

where q is the atomic density, Dx is the distance betweenthe q concentration data points in the proxigram, ck

i isthe concentration of an element i at each data point andk = a on the a-Al matrix side and k = h0 on the precipitateside of the heterophase interface.

From the Gibbs adsorption isotherm for a system withtwo phase and n P 3 components [52], a coefficient forthe reduction of interfacial free energy (c) at a concentra-tion ci due to segregation of component i at the hetero-phase interface, assuming a dilute solution model, isgiven by [49,50,53,54]:

@c@ci

����T ;P ;l1;...;li�1;liþ1;...;ln

¼ �kBTCcri

i

cið3Þ

where Henry’s law for dilute solution is assumed, li is thechemical potential of component i, kB is Boltzmann’s con-stant and T is the absolute temperature. As to the interfa-cial Sc segregation in the present Al–Cu–Sc alloys, thereduction in c due to the interfacial Sc solute excess canbe calculated by evaluating the following integral [55]:

� 1

kBTCrelSc

Z cfinal

cinitial

dc ¼Z cfinal

Sc

cinitialSc

dcSc

cScð4Þ

Here cinitialSc and cfinal

Sc are the Sc concentration in the a-Almatrix and the peak concentration of Sc at the h0/a-Al ma-trix interface, respectively.

Using the 3DAP experimental data on concentrations,the reduction in interfacial free energy (Dc) caused by Scsegregation at the h0/a-Al matrix interfaces can be quanti-tatively evaluated from Eqs. (1)–(4). The determined Dcare ��13.1, �42.3 and �17.6 mJ m�2 for the Al–Cu–Scalloys aged at 473, 523 and 573 K for 3 h, respectively, aslisted in Table 2. Note that the plate-like h0 precipitateshave coherent interface (CI) to the a-Al matrix along theirbroad flat faces and semi-coherent interface (SCI) at theirperiphery. As mentioned before, we merely captured the3DAP images/data for the coherent interfaces (see Fig. 5)and failed to access to the semi-coherent interfaces, dueto large radius of the h0 precipitate and small areal fractionof the semi-coherent interface. The Dc quantitatively deter-mined here is that for the coherent interfaces DcCI . Biswaset al. [15] have made first attempt to quantitatively assessthe difference between CI solute segregation and SCI solutesegregation at the h0 precipitate, and found that the Dc for

Table 2Summary of the calculations on Dc caused by interfacial Sc segregation inthe Al–Cu–Sc alloys.

T (K) 473 523 573Dc (mJ m�2) –13.1 ± 2.5 –42.3 ± 3.4 –17.6 ± 1.8

the SCI is approximately five times greater than that for theCI. Simply, we will used a scaling factor j to estimate thereduction in SCI interfacial energy, i.e. DcSCI = jDcCI.

Previous atomic simulations on h0 precipitate in Al–Cualloys [32] have given the interfacial free energy ofcCI = 170 mJ m�2 for the CI and cSCI = 520 mJ m�2 forthe SCI. Refer to DcCI = –42 mJ m�2 evaluated for the523 K-aged Al–Cu–Sc alloy, it is striking to find a �25%reduction in the interfacial energy caused by the interfacialSc segregation. Kirchheim’s thermodynamic calculations[56] have clearly demonstrated that solute segregation atgrain boundary, by decreasing the grain boundary energy,can reduce the grain size of polycrystalline materials andtake advantage of the hardening effect of grain boundaries.The inhibition of grain growth is mainly related to thereduction in driving force for grain coarsening (a resultof decreased grain boundary energy) rather than the solutedrag effect [56]. Similarly, theoretical predictions [57,58]also revealed that excess solute at the precipitate/matrixinterface can stabilize the size of precipitates. These calcu-lations support our present experimental results that pre-cipitate size is reduced when Sc is added and segregatedat the precipitate/matrix interface, especially in the523 K-aged Al–Cu–Sc alloy where the strongest interfacialSc segregation or the most decrease in interfacial energy isaccompanied by the most pronounced reduction in precip-itate size. Since the deformation behaviors of heat-treatableAl alloys is closely dependent on the precipitate size anddistribution that are in turn controlled by the interfacialenergy, the variation in interfacial energy caused by inter-facial Sc segregation will have a marked impact on thestrengthening effect and fracture mechanism, as discussedbelow.

4.2. Effect of interfacial Sc aggregation on strengthening

effect

Experimental results have revealed that the strengthen-ing effect in present Al–Cu–Sc is predominantly contrib-uted by the h0 precipitates. Some models have beenproposed [21,59–63] to quantitatively describe the strength-ening effect of plate-like precipitate. The interparticle spac-ing kp between the plate-like precipitates, which is usuallyrelated to the size (rp), volume fraction (fp) and numberdensity (Nf) of the precipitates, is believed to be the key fac-tor in precipitation strengthening. Although precipitationstrengthening is also strongly impacted by the heterophaseinterfaces between the matrix and precipitates, the effect ofheterophase interfaces has been barely taken into accountin these models. The reason is that the character of hetero-phase interfaces is hard to be characterized in a quantita-tive way. In this paper, by using the advanced 3DAP andadopting the analytical method proposed by Seidman’sgroup, we have quantified the changes in interfacial energyunder different interfacial Sc segregation. It is then possibleto make an attempt to correlate the interface energy tomechanical properties simply but directly.

B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1687

Extensive studies on the diffusional growth of plate-likeprecipitates have shown that the precipitate lengtheningrate is constant in time [33,64] prior to soft impingementof adjacent neighbor precipitates (soft impingement is sche-matically illustrated in Fig. 9a). The Zener–Hillert expres-sion for the lengthening rate is given by [47,48,65]:

drp

dt¼ DCu

2 � Rp

caCu � ch0=a

Cu

ch0Cu � ch0=a

Cu

1� Rc

Rp

� �ð5Þ

where DCu is the Cu solute diffusivity, ch0=aCu is the Cu con-

centration in the matrix at the precipitate/matrix growinginterface, Rp is the radius of the plate tip and Rc is the platetip radius at which growth would stop because capillary ef-fects reduce the driving force for Cu diffusion to zero[47,48]. According to Zener [48], the radius of the diffusionzone around the plate tip (Rdz, see Fig. 9a) is proportionalto the plate tip radius Rp. Hillert [47] found that the pro-portionality between Rdz and Rp is �2, i.e. Rdz = 2Rp. Ze-ner further proposed a maximum growth rate hypothesis[48] that the stable plate lengthening conditions will onlyprevail for values of Rp close to that yielding the maximum

Δσ0Al

-Cu-

Sc /

Δσ0Al

-Cu

σ int /

σG

ND

(a)

(c)

(b)

(d)

Fig. 9. (a) Sketch illustrating soft impingement of adjacent h0 plates (indicateplates represent h0 precipitates, purple surrounding represents solute diffusion fido not reach soft impingement, as indicated by open arrows. (b) Calculationcomparison with experimental results. (c) Sketches illustrating interfacial dinterfaces under a critical stress rint (the upper one), and the generation of geomincompatibility between h0 precipitate and Al matrix (the bottom one). (d) Calmeans that the local stress caused by GNDs will exceed rint and hence induce ithe matrix Al will be finally rupture due to the excess storage of GNDs. (Forreferred to the web version of this article.)

growth rate. The maximum growth rate is achieved forRp = 2Rc [47,48]. The critical plate tip radius Rc is, in turn,a function of interfacial energy of the plate tip cSCI and theonset driving force DGv as Rc n cSCI=DGv [66]. Therefore, theinterparticle spacing between adjacent precipitates can beexpressed in terms of cSCI and DGv:

kp ¼ 2Rdz ¼ 2 � ð2RpÞ ¼ 2 � ð2 � ð2RcÞÞ ¼8LcSCI

DGvð6Þ

where L is a constant to reflect the homogeneity of precip-itate size and dimensional distribution. In the case of per-fectly monotonic precipitate size distribution andperfectly random site distribution, L is expected to be closeto 1 and kp has the minimum value of kmin

p [61]. In reality,however, not all precipitate plate tips will impinge on an-other plate at exactly the same time. As demonstrated inFig. 9a, although several plates have reached the conditionof soft impingement, several other have not yet. This willcause L to be greater than 1 and kp > kmin

p . The value ofL captures this effect and is expected to increase with thewidth of the precipitate size distribution [61].

460 480 500 520 540 560 5801.0

1.5

2.0

2.5

3.0Calculations

κ = 3κ = 5κ = 7

Aging temperature (K)

Experimental data

0 100 200 300 400 5000.0

0.5

1.0

1.5

2.0

2.5

3.0

Precipitate radius rp (nm)

473 K 523 K 573 K

Interfacial decohesion

d by solid arrows) and definition of parameters of Rp, Rdz, and kminp . Red

eld, and blue background represents the Al matrix. Note that some platess on normalized DrAl–Cu–Sc

0 =DrAl–Cu0 as a function of aging temperature, in

ecohesion and concomitantly interface void formation at the h0/matrixetrically necessary dislocations (GNDs) to accommodate the deformation

culation of rint/rGNDs as a function of precipitate radius rp. rint/rGNDs < 1nterfacial decohesion. Otherwise, interfacial decohesion hardly occurs andinterpretation of the references to color in this figure legend, the reader is

1688 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

Substituting Eq. (6) into the Orowan equation leadsdirectly to a relationship between the precipitationstrengthening and the precipitate/matrix interfacial energy:

Dr0 / Ds / lbkp/ lbDGv

8LcSCIð7Þ

where l is the shear modulus of the matrix and b is the Bur-gers vector. Simply assuming that L and DGv are constantand insensitive to the change in cSCI, the above equationcan show the dependence of precipitation strengtheningincrement on the reduction in cSCI caused by interfacialSc segregation. Normalizing the peak-aged Dr0 of Al–Cu–Sc alloys by that of their Sc-free counterparts, someunknown parameters can be divided out and a reducedexpression will be obtained as:

DrAl�Cu�Sc0

DrAl�Cu0

����T

¼ cSCI þ DcSCI

cSCI

����T

ð8Þ

The subscript T in the above equation represents theaging temperature. Using the values of DcSCI determinedbefore, the normalized Dr0 can be calculated as a functionof aging temperature or DcSCI. Calculations are in broadagreement with the experimental results, referring to thecomparison in Fig. 9b.

At this point, it should be specially mentioned that thestrengthening response is directly determined by the precip-itate size, content and distribution. The influence of interfa-cial energy on strengthening response is actuallyimplemented by affecting the precipitation. The derivationof Eq. (8) is aimed at correlating the strengthening responsewith the interfacial energy (characterizing the degree ofinterfacial solute segregation) in an intuitive and semi-quantitative manner, which may be helpful for theory-assisted alloy design of new microalloyed Al alloys withhigh performance.

4.3. Effect of interfacial Sc segregation on the size-dependent

fracture mechanism

Interfacial decohesion has been experimentally revealedin the Al–Cu–Sc alloy aged at 523 K for a prolonged time,which is responsible for the sharp reduction in ductility.The nucleation of cavities at the particle/matrix interfacecaused by plastic deformation has been studied numeroustimes and some criteria have been proposed, see Ref. [67]by Goods and Brown and references therein. Any energy-based model, including the critical stress and the criticalstrain ones, should consider the effect of interface energyof the particle/matrix interfaces, because the interfacialdecohesion involves the creation of new surfaces of matrixmaterial and particles, as well as the disappearance of par-ticle/matrix interface. Sun [68] has developed an interfacialdecohesion model to derive the critical stress (rint) requiredfor void initiation at the interface, where the energy bal-ance condition was obtained by applying the concept ofenergy release rate in linear elastic fracture mechanics.

The interfacial decohesion strengths obtained from thismodel fit well with those measured experimentally inspheroidized steels that contain sub-micron-sized particles[68]. The present h0 precipitates have a radius at the samesub-micron level; we extend Sun’s model to account forthe interfacial decohesion at the plate-like h0 precipitates(Fig. 9c), which yields an expression for the interfacialstress rint as

rint ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Em þ Ep

2

� �pctotal

rpð1� v2Þ

sð9Þ

where Em = 70 GPa [25] and Ep = 180 GPa [69] are theelastic moduli of the matrix and the h0 precipitate, respec-tively; v = 0.3 is Poisson’s ratio; and ctotal is the totalchange in surface/interfacial energy caused by interfacialdecohesion, i.e.

ctotal ¼ csurAl þ csur

h0 � cCI ð10Þ

Here csurAl and csur

h0 are the surface free energy of Al and h0

that have values of �1.0 and �2.5 J m�2 [70], respectively.Eqs. (9) and (10) show that rint varies inversely with bothprecipitate size rp and h0/matrix interfacial energy cCI. Thismeans that the plate-like h0 precipitates with greater sizeand/or higher interfacial energy are more apt to sufferinterfacial decohesion under plastic deformation.

However, the trigger of interfacial decohesion requiresthat the local stress reaches rint. Generally, the local stressunder plastic deformation consists mainly of applied exter-nal stress, hydrostatic tensile stress and local flow stressthat is induced by the geometrically necessary dislocations[67]. Due to the deformation incompatibility between theAl matrix and h0 precipitate, gradients of deformation formand geometrically necessary dislocations (GNDs) areinduced to accommodate the deformation gradients[71,72]. The density of GNDs (qGND) is closely dependenton the interparticle spacing kp between the h0 precipitates[25,72]:

qGND ¼elocal

4bkpð11Þ

where elocal is the local shear strain and the expression forkp has been given in Eq. (6). The local flow stress causedby GNDs is then given by

rGND ¼ glbðqGNDÞ1=2 ¼ gl

belocalDGv

32LcSCI

� �1=2

ð12Þ

where g is a constant of order of 1. Since Al alloys have rel-atively lower strength (or lower applied stress), the localstress is predominantly contributed by rGND, especiallywhen kp is nano-size as in the present work. We can simplydefine the criterion for interfacial decohesion of h0 precipi-tate as:

rGND P rint; or rint=rGND 6 1 ð13ÞEqs. (12) and (13) reveal that the lower the value of cSCI,the greater is rGND. This means that interfacial decohesion

0 100 200 300 400 5000.0

0.2

0.4

0.6

0.8

1.0ε f

Precipitate size rp (nm)

rp

cri

Regime I Regime II

Fig. 10. Precipitate size-dependent fracture mechanism map of theAl–Cu–Sc alloy aged at 523 K. Two regimes, I and II, are divided by acritical size of rcri

p � 200 nm. In regime II, interfacial decohesion at the h0/matrix interfaces is ready to happen and the fracture mechanism is crackpropagation aided by interfacial voids (right insert). In regime I, localstress is not enough to trigger the interfacial voiding and the fracturemechanism is predominantly matrix Al rupture (left insert). Note that thematrix undergoes more intense plastic deformation in the case of I, whichresults in higher ductility. The dark blue color in the background of theleft insert indicates more intense deformation compared with the light bluecolor of the right insert. (For interpretation of the references to color inthis figure legend, the reader is referred to the web version of this article.)

B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690 1689

is most possible to happen in the 523 K-aged Al–Cu–Sc al-loy, because the most pronounced interfacial Sc segrega-tion in this alloy causes the most reduction in cSCI. Inaddition, interfacial decohesion is more likely to occur inthe case of greater precipitate size, as mentioned before.

For quantitative reasons, rint/rGND is calculated as afunction of precipitate size rp for the Al–Cu–Sc alloys agedat 473, 523 and 573 K, respectively. Some values of param-eters [17,21] for calculations include l = 28 GPa,b = 0.286 nm, the maxim elocal � 0.4 and DGv

� 100 kJ mol�1 that was previously determined in Al–Cualloys [73]. The calculations are shown in Fig. 9d. rint/rGND < 1 is found in the 523 K-aged Al–Cu–Sc alloy whenrp is greater than �200 nm, indicative of interfacial decohe-sion thereafter. While in the 473 and 573 K-aged Al–Cu–Scalloys, rint/rGND is constantly larger than 1, which indi-cates that the crack propagation is mainly through matrixfracture rather than interfacial decohesion in the twoalloys. These calculations are consistent with the experi-mental results.

The interfacial Sc segregation is now proven to have adual effect on the ductile fracture of Al–Cu–Sc alloys. Onthe one hand, the reduction in interfacial energy causedby the Sc segregation increases the critical interfacial stress,which prevents the interfacial decohesion. On the otherhand, narrower distribution of h0 precipitates with finer sizeis induced by the interfacial Sc segregation, which producesmore GNDs around the precipitates and as a result greaterlocal stress under applied loading. A competition thusexists between the two contrary effects, which is tailoredby both the interfacial energy and the precipitate size.When the local stress is greater than the critical interfacial

stress in the conditions of lower interfacial energy andlonger precipitate size, the fracture mechanism is interfacialdecohesion-aided crack growth that results in low ductility.Otherwise, the fracture mechanism is predominantly Almatrix rupture, accompanied with high ductility. The tran-sition in fracture mechanisms is just observed in the 523 K-aged Al–Cu–Sc alloy. Fig. 10 shows the size-dependentfracture mechanism map in this alloy. The critical sizercri

p � 200 nm divides the map into two regimes, I and II,which display different deformation behaviors and fracturemechanisms.

5. Conclusions

(1) Sc segregation at the h0/matrix interfaces has beencharacterized by using 3DAP. This interfacial solutesegregation, limiting the precipitate growth and pro-moting the precipitate nucleation, results in narrowdistribution of h0 precipitates with reduced sizes.

(2) Interfacial Sc segregation in 523 K-aged Al–Cu–Scalloy is more pronounced than in both 473 and573 K-aged alloys. This is related to the two require-ments for interfacial solute segregation, i.e. enoughSc diffusion rate and available free Sc atoms, whichcan be met in the 523 K-aged alloy but only partiallymet in the two other temperature aged alloys.

(3) Reduction in interfacial energy caused by Sc segrega-tion has been evaluated quantitatively and the 523 K-aged Al–Cu–Sc alloy has the greatest reduction ininterfacial energy. This can well interpret the higheststrength observed in the 523 K-aged alloy, based onthe relationship between precipitation strengtheningand interfacial energy.

(4) A sharp decrease in ductility has been found in the523 K-aged Al–Cu–Sc alloy at a critical precipitatesize of �200 nm. This was experimentally found tobe caused by the interfacial decohesion at the h0/matrix interfaces ahead of the main crack. A micro-mechanical model, taking into account the effect ofboth interfacial energy and precipitate size, has beendeveloped to rationalize the interfacial decohesionthat is related to the interfacial Sc segregation.

Acknowledgements

This work was supported by the National Natural ScienceFoundation (51171142), the National Basic Research Pro-gram of China (973 program, Grant Nos. 2010CB631003and 2012CB619600) and the 111 Project of China(B06025). GL thanks the financial support of FundamentalResearch Funds for the Central Universities and TengFeiScholar project. RHW thanks the support of NaturalScience Foundation of ShaanXi Province of China(2010JK758). We also thank W. Q. Liu (Shang Hai Univer-sity) for his assistance in 3DAP experiments.

1690 B.A. Chen et al. / Acta Materialia 61 (2013) 1676–1690

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